The volumetric change (AV) is dependent on changes in pressure and 

 temperature that the hull experiences in going from the surface to some 

 depth. Thus 



AV = AV + AVt 



'.(t^^"„A,) 



where AVp = change in volume due to pressure 



AV^ = change in volume due to temperature 



Vq = initial volume at zero pressure 



AP = change in pressure 



Kq = effective bulk modulus of the hull = P/IV/Vq) 



ct^y = volumetric coefficient of thermal expansion for the hull 

 and its material 



At = change in temperature 



An accurate determination of bulk modulus (K^) requires volumetric 

 calculations based on changes in hull dimensions due to pressure effects. The 

 value of the bulk modulus used for configurations under consideration was 

 4x lO^psi. 



The coefficient of thermal expansion for the hull is dependent on the 

 hull material and was taken as 0.1 17 x 10'"'*/°C for steel. The maximum 

 temperature change applied to the analysis was 1 1 .7°C. 



The change in density is also dependent on pressure and temperature 

 changes plus the effects of salinity variations. Two methods were used in the 

 buoyancy analysis to determine the change in density. In the first method 

 density was determined from 



62.42 

 d = 



d = 



where d = density, Ib/ft"^ 



V = specific volume 

 AV = change in volume 



62.42 AV 



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